Im new to knitting and I got a book of several small swatch patterns that when finished measure about 12x12. Lets say I want to make an afghan with ONE of those swatches, do I just double or triple the pattern like i would do with a cooking recipe? And would it work the same way with amigurumi?

Pretty much, though you have to take a couple things into consideration. If there's a repeating stitch pattern, you need to add stitches in increments of the repeats inside the edge stitches. You can sometimes increase a little with larger needles, or if you use really large needles and doubled yarn that can work. Or you can do a combination.

Figure out the sts per inch with the yarn and needles you want to use, then multiply the sts per inch times the width you want, then adjust the number if you need it to fit a stitch pattern repeat.